M22 galaxy

In TNG: "Where no one has gone before, the traveller sends the Enterprise D over 2,000,700,000 light years to the M22 Galaxy

LaForge estimates it would take 300 years to get home, and that a subspace transmission would be recieved by starfleet in 51 years.

But in Voyager, they are sent a mere 70,000 light years by the caretaker, and say it would take 10 years to get home.

The Enterprise went over 28581 times as far as Voyager, so shouldn't a subspace message from Voyager have been recieved by starfleet in a couple of days at most? And shouldn't it only have taken a couple of weeks to get home?

Nitpick: the galaxy in question is actually M33, or Triangulum, up to 3 million ly away (although Data's 2.7 million ly is an acceptable estimate as well, since the E-D was only said to have ended "on the far side" of M33, not necessarily meaning "through M33 and out the other side"). M22 would be a globular cluster within the Milky Way, just 10,000 ly away. So Picard is actually facing a journey just 38.5 times longer than Janeway.

In both the TNG episode and the VOY pilot, a central issue is that the distance would take X years to span "even at maximum velocity". In both cases, it is implied that it would be impossible to travel at maximum velocity in practice. We never get a clear quote for what the theoretical maximum velocity of the E-D or the Voyager might be, only conjectural datapoints about "cruise velocity" or "redline".

So Picard facing a travel time 4.2 times longer for a distance 38.5 times longer is by no means a major discrepancy. Perhaps the theoretical top speed of Picard's ship is simply nine times higher than Janeway's?

As for subspace message travel time, there's something fishy about that "51 years" thing to start with. It's not really 51 years - it's "51 years, 10 months, 19 weeks, 16 days -" which defies conventional logic because 19 weeks is longer than a month and 16 days is longer than a week. So it very much sounds as if Data is listing a range of possibilities: "51 years for condition X, 10 months for condition Y, 19 weeks for condition Z, 16 days for condition-" before Picard cuts him off in disgust. And since Picard indeed does that, it may well be that none of the conditions could ever be met in practice. VOY makes it pretty clear that subspace messages just plain don't carry all that far.

(Or perhaps they do travel across millions of ly - but only if there aren't galaxies and stars in between to disrupt the subspace landscape?)

According to TOS: "That Which Survives" the Enterprise covered 1000 lightyears in 12 hours at warp 8.4. They would have made Voyager's journey in about a month. They also made it as far as the rim of the galaxy ("Were No Man...") and the centre twice ("Megas Tu" and STV, the latter explicitly launching from Earth)

Trek writers just pull the numbers out of thin air for time, distance and speed. It's speed of plot. They never use the charts or formulas in the technical manuals.

Well, it makes a lot of sense that long trips would have to be conducted at a lower average speed than short ones. Ships "tire" just like runners. Covering 100 m in ten seconds doesn't mean you could cover 100 km in ten thousand seconds or under three hours.

Four days to Vulcan in ST:TMP is a bit slow in terms of even the average TOS or TNG travel times, ignoring the outliers. Possibly Scotty was telling Spock how sorry he was that the ship was so tasked and damaged that it would take four full days to get the Vulcan back "home"?